Title:

Lognormality, δκ ~ κ δφ, EGS, and All That

Authors:

Peter LEARY, Peter MALIN, Justin POGACNIK, John RUGIS, Brice VALLES, Peter GEISER

Key Words:

EGS, fractures, permeability enhancement, Biot coupling, geocriticality

Conference:

Stanford Geothermal Workshop

Year:

2014

Session:

Enhanced Geothermal Systems

Language:

English

Paper Number:

Leary

File Size:

4620 KB

View File:

Abstract:

Enhanced/Engineered Geothermal System (EGS) commercial hot-fluid production requires controlled well-to-well flow stimulation over distances on the order of 100m well-to-well offsets at well-flow rates exceeding all but the most productive of oil field wells. Such flow stimulation goals have not been achieved by a succession of ‘proto’-EGS projects to date. We argue for a new perspective on in situ flow stimulation based on well-log, well-core and well-flow empirics heretofore ignored in EGS thinking. The new perspective emerges from the following logic: I. Earlier proto-EGS project thinking assumed that in situ rock properties, and by extension its fluid flow properties, are de facto spatially uncorrelated. That is, rock and rock-fluid interactions were taken as effectively smoothly-varying spatially-average continuum properties with spatial variations more-or-less confined to largely knowable bounds. Flow enhancement was to be achieved by establishing new in situ porosity/permeability via cleaving the material continuum into sections defined by discrete planar discontinuities of unit porosity and high permeability through which fluids rapidly pass in an otherwise quasi-uniform material continuum of low permeability. II. Attempts to achieve controlled in situ well-to-well flow connection via discrete planar discontinuities generated by pressurised wellbore fluids has proved unproductive. Pressurised wellbore fluids were instead observed to invade the rockmass in a mélange of essentially uncontrolled, and often unpredictable, widely-disseminated flow paths with little or no prospect of attaining significant well-to-well flow at required offsets. III. In parallel with successive failures to section rock with discrete planar discontinuities affording controlled well-to-well flow, a great deal of well-log, well-core and well-flow data were seen to show that (i) in situ rock properties, in particular porosity, are de facto spatially and erratically correlated over decades of scale length from grains to reservoirs; (ii) in situ permeability is essentially controlled by in situ porosity and as such fluctuates spatially and erratically over decades of scale length; and (iii) in situ flow systems are lognormally rather than the normal distributions expected for an essentially uniform material continuum. IV. More particularly, well-log, well-core and well-flow data can be organized into three widely attested and robust features of in situ rock and associated flow: a. Spatial correlation for which well-log Fourier power-spectra scale inversely with spatial frequency k, S(k) ~ 1/k , ~1/km < k < 1/cm (S(k) ~ const is a necessary, and sufficient, condition for uncorrelated spatial fluctuations); b. Rock-fluid interaction via a feedback loop in which spatial fluctuations in permeability κ are proportional to existing permeability and spatial fluctuations of porosity φ, δκ ~ κ δφ; c. Lognormal flow system distribution in which a few high-flow systems dominate a large number of low-flow systems, κ ~ exp(αφ), with empirical integration constant observed to be much larger than unity, α >> 1. V. For purposes of rock-fluid interaction, the above characterization of in situ rock has spatially fluctuating porosity φ(x,y,z) as the chief material property of interest, and invites expressing rock-fluid coupling in terms of the permeability-porosity physical feedback relation δκ ~ κ δφ, with the recognition that this feedback relation provides a natural route to a rock-fluid m


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